scholarly journals Analytic solutions of a linear functional equation

1969 ◽  
Vol 21 (3) ◽  
pp. 297-303
Author(s):  
Marek Kuczma
Keyword(s):  
Functional Equation ◽  
Linear Functional ◽  
Analytic Solutions ◽  
Linear Functional Equation

scholarly journals Series Solution of a Functional Equation

1965 ◽  
Vol 5 (1) ◽  
pp. 48-55
Author(s):  
W. Pranger
Keyword(s):  
Functional Equation ◽  
Linear Operator ◽  
Operator Theory ◽  
Inversion Formula ◽  
Linear Functional ◽  
Series Solution ◽  
Analytic Solutions ◽  
Linear Functional Equation ◽  
General Operator ◽  
Image Position

In this we will study analytic solutions to the linear functional equation where f and h are given functions, x is a given complex number and the function g is to be found. This is a generalization of Schröder's functional equation. The results obtained are global in nature and the solutions holomorphic. The equation will be viewed from the standpoint of linear operator theory. When studied in this manner one arrives at a general operator inversion formula.

On a linear functional equation

1989 ◽  
Vol 38 (2-3) ◽  
pp. 113-122 ◽  
Author(s):  
László Székelyhidi
Keyword(s):  
Functional Equation ◽  
Linear Functional ◽  
Linear Functional Equation

scholarly journals The Generalized Pomeron Functional Equation

2019 ◽  
Vol 2019 ◽  
pp. 1-4
Author(s):  
Yong-Guo Shi
Keyword(s):  
Functional Equation ◽  
Continuous Function ◽  
Linear Functional ◽  
Continuous Solution ◽  
Suitable Condition ◽  
Single Parameter ◽  
Linear Functional Equation ◽  
Continuous Solutions ◽  
Constant Coefficients

This paper investigates the linear functional equation with constant coefficients φt=κφλt+ft, where both κ>0 and 1>λ>0 are constants, f is a given continuous function on ℝ, and φ:ℝ⟶ℝ is unknown. We present all continuous solutions of this functional equation. We show that (i) if κ>1, then the equation has infinite many continuous solutions, which depends on arbitrary functions; (ii) if 0<κ<1, then the equation has a unique continuous solution; and (iii) if κ=1, then the equation has a continuous solution depending on a single parameter φ0 under a suitable condition on f.

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